Related papers: Regularity criteria with angular integrability for…
In this paper, we generalize the main results of [1] and [31] to Lorentz spaces, using a simple procedure. The main results are the following. Let $n\geq 3$ and let $u$ be a Leray-Hopf solution to the $n$-dimensional Navier-Stokes equations…
In this paper, we continue our work in [15] to derive {\epsilon}-regularity criteria at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. We establish a $\varepsilon$-regularity criterion below of…
In this paper, we investigate the link between kinetic equations (including Boltzmann with or without cutoff assumption and Landau equations) and the incompressible Navier-Stokes equation. We work with strong solutions and we treat all the…
In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if $(u,p)$ is a…
In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary…
We study smooth solutions to the three-dimensional stationary Navier--Stokes equations and establish new Liouville-type theorems under refined decay assumptions. Building on the work of Cho et al., we introduce a refinement to previously…
We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to -1. Our results rely on…
In this paper we consider the three-dimensional Navier-Stokes equations in infinite channel. We provide a regularity criterion for solutions of the three-dimensional Navier-Stokes equations in terms of the vertical component of the velocity…
In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier--Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria…
The axially symmetric solutions to the Navier-Stokes equations in a periodic cylinder with boundary slip conditions on the lateral part of its boundary are considered. A priori estimates for solutions with large swirl necessary for a proof…
This work studies the system of $3D$ stationary Navier-Stokes equations. Several Liouville type theorems are established for solutions in mixed-norm Lebesgue spaces and weighted mixed-norm Lebesgue spaces. In particular, we show that, under…
We study regularity criteria for the $d$-dimensional incompressible Navier-Stokes equations. We prove if $u\in L_{\infty}^tL_d^x((0,T)\times \mathbb{R}^d_+)$ is a Leray-Hopf weak solution vanishing on the boundary and the pressure $p$…
We prove partial regularity of suitable weak solutions to the Navier--Stokes equations at the boundary in irregular domains. In particular, we provide a criterion which yields continuity of the velocity field in a boundary point and obtain…
We investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is an improved Lipschitz regularity estimate at scales larger…
H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space $\R^3$ based on two velocity components. Recently, one of the present authors extended this result…
The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier--Stokes solutions do not develop singularities. This provides an alternative to the approach of \cite{Grujic2013}, which is based on…
Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively…
We establish several boundary $\varepsilon$-regularity criteria for suitable weak solutions for the 3D incompressible Navier-Stokes equations in a half cylinder with the Dirichlet boundary condition on the flat boundary. Our proofs are…
We extend Barker's weak-strong uniqueness results for the Navier--Stokes equations and consider a criterion involving Besov spaces and weighted Lebesgue spaces.
This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point $z$ if its…